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Let's go through each of these polynomial expressions to factor them:

1. **\( w^2 - 9 \)**
   - This is a difference of squares: \( w^2 - 9 = (w - 3)(w + 3) \).

2. **\( w^2 - 8w + 16 \)**
   - This is a perfect square trinomial: \( w^2 - 8w + 16 = (w - 4)(w - 4) = (w - 4)^2 \).

3. **\( 9w^2 - 16 \)**
   - Again, this is a difference of squares: \( 9w^2 - 16 = (3w - 4)(3w + 4) \).

4. **\( 25w^2 + 40w + 16 \)**
   - This is also a perfect square trinomial: \( 25w^2 + 40w + 16 = (5w + 4)(5w + 4) = (5w + 4)^2 \).

Let me know if you need further clarification or more details on any of these factorizations.

Here are 5 related questions for practice:
1. How do you factor a difference of cubes like \( x^3 - 8 \)?
2. How do you identify a perfect square trinomial?
3. What method do you use to factor a trinomial that isn’t a perfect square?
4. How can you factor a polynomial when the leading coefficient is not 1?
5. How do you solve a quadratic equation by factoring?

**Tip**: When factoring, always check if a polynomial is a perfect square or if it’s a difference of squares first—it simplifies the process!

Rewrite each of the following polynomial expressions in factored form: w^2 - 9, w^2 - 8w + 16, 9w^2 - 16, 25w^2 + 40w + 16

Learn how to factor polynomial expressions like w^2 - 9, w^2 - 8w + 16, 9w^2 - 16, and 25w^2 + 40w + 16. This problem covers algebraic concepts such as the difference of squares and perfect square trinomials. Ideal for students in Grades 9-11.

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